Can you add leverage to an existing trade?

Lets say I buy XYZ at 132.10 without any leverage...

XYZ goes up a little ways to 132.20, can I add a leverage to this position, like 10:1 or something?

Or can you only add leverage before the purchase?

On the live exchanges for shares you cannot use leverage and in terms of futures contracts, you will automatically be using leverage when you enter a positional trade using most brokers, i can't imagine you'd even enter a position without leverage.
With shares, leverage doesn't exist except in the form of Spreadbetting and CFD's and you, as an American cannot use such products.
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What exactly are you trading?

I think you may have confused margin with leverage maybe?

So is margin the cash that you put down and leverage is what you borrow to increase the value of your position?

So let me get this right? You want to walk into a bookie, place a bet and if you know this bet is going to come off you want to increase your risk and still get the same odds. No chance. If you want to risk more on the trade you need to open a new bigger position.

which may involve higher or lower leverage than before

yes, something like this,

if we typically use the purchase of a house as an example,

the amount you put down as a deposit for it, in the trading/investing world, this would equate to your margin. the bank would then 'loan' you the remainder of the money to cover the value of the house, so that you may buy it.

in essence this 'loan' will be 'x' amount of your yearly salary, in otherwords the leverage the bank is going to give you.

you then pay back this borrowed amount to ultimately 'own' the house, in trading/investing, you dont pay this loan back unless you want to take physical delivery of the asset.

however in both circumstances, you are directly responsible for loss of equity on cash out.

This isn't the same, at all.